10:45 AM - 12:15 PM
[HDS06-P11] Development of a Nonlinear Inversion Method Using Nonlinear Long Wave Equation and Levenberg-Marquardt Method
Keywords:Tsunami, Non-linear inversion, Levenberg-Marquardt method
Historical documents have repeatedly recorded large earthquakes in the Nankai Trough since the 7th century. It is important to conduct research based on past earthquakes to predict future large earthquakes in the Nankai Trough. While there were many studies to estimate earthquake source models using linear tsunami inversion, few studies used nonlinear inversion. In the limited examples of nonlinear inversion, they estimated it by repeating the linear inversion while adjusting the nonlinearity. This study proposes a complete nonlinear inversion method for tsunami trace heights by iteratively solving nonlinear long-wave equations using a high-performance computer and the Levenberg-Marquardt method.
We applied the new nonlinear tsunami inversion to estimate the fault slip during the 1946 Nankai earthquake. We created eight subfaults referring to the N3 and N4 seismic segments in Annaka et al. (2003). The tsunami calculation used the nonlinear long-wave equations on three topographic nesting layers gridded by 18, 6, and 2 arc-sec intervals. The integral time was 3 hours with a time width of 0.1 s. Observed tsunami height stemmed from a database of Tohoku University. In the iterative inversion, we used highly reliable (A) data higher than 50 cm above the sea level and less than 100 m run-up distance. The total number of tsunami trace heights was 122. The geometric mean K and the geometric standard deviation κ from Aida (1978) indicated a degree of fitting. We also calculated the residual sum of squares between observation and calculation in the tsunami heights.
Our obtained fault model showed a larger slip than the models previously proposed in the region off Shikoku and Kii Channel, with a maximum slip of 7.2 meters. The seismic moment was calculated to be 6×10^21 (N·m), which is higher than the 3.5×10^21 (N·m) in Baba et al. (2005) and comparable to the 7×10^21 (N·m) in Annaka et al. (2003). Our new slip model of the 1946 Nankai earthquake explained the observed tsunami heights well. The K-κ and the residual sum of squares for the calculated values and trace heights were 0.99-1.26 and 43.8 m^2, while Annaka et al. (2003) model, these were 1.08-1.37 and 82.6 m^2. The residual sum of squares was improved by 47 %.
We applied the new nonlinear tsunami inversion to estimate the fault slip during the 1946 Nankai earthquake. We created eight subfaults referring to the N3 and N4 seismic segments in Annaka et al. (2003). The tsunami calculation used the nonlinear long-wave equations on three topographic nesting layers gridded by 18, 6, and 2 arc-sec intervals. The integral time was 3 hours with a time width of 0.1 s. Observed tsunami height stemmed from a database of Tohoku University. In the iterative inversion, we used highly reliable (A) data higher than 50 cm above the sea level and less than 100 m run-up distance. The total number of tsunami trace heights was 122. The geometric mean K and the geometric standard deviation κ from Aida (1978) indicated a degree of fitting. We also calculated the residual sum of squares between observation and calculation in the tsunami heights.
Our obtained fault model showed a larger slip than the models previously proposed in the region off Shikoku and Kii Channel, with a maximum slip of 7.2 meters. The seismic moment was calculated to be 6×10^21 (N·m), which is higher than the 3.5×10^21 (N·m) in Baba et al. (2005) and comparable to the 7×10^21 (N·m) in Annaka et al. (2003). Our new slip model of the 1946 Nankai earthquake explained the observed tsunami heights well. The K-κ and the residual sum of squares for the calculated values and trace heights were 0.99-1.26 and 43.8 m^2, while Annaka et al. (2003) model, these were 1.08-1.37 and 82.6 m^2. The residual sum of squares was improved by 47 %.